The deal includes an £8m loan fee and Roma will be covering the 30-year-old Belgium international’s wages.
Inter Milan had hoped Lukaku, who is not part of Mauricio Pochettino’s plans at Chelsea, would return to the club where he spent last season on loan.
But the forward was unhappy coach Simone Inzaghi did not start him in the Champions League final.
Juventus were also keen to sign Lukaku but were unable to make the changes required to their squad.
There are still some details to be finalised but the agreement for his return to Italy is essentially done.
A source close to Roma owners the Friedkin family, who took over the club in 2020, said the transfer demonstrated their commitment and desire to “achieve the glory the club and the fans deserve”.
The move to Roma means Lukaku will be reunited with Jose Mourinho, who persuaded him to join Manchester United ahead of Chelsea when he moved to Old Trafford from Everton in 2017.
Lukaku moved back to Chelsea from Inter Milan for £97.5m in August 2021 on a five-year-deal for his second spell at Stamford Bridge, but has struggled to establish himself and this season has been training away from the first team.
He has scored 15 goals in 59 games for the Blues in two spells.
“When he is conditioned and fit he is a real handful,” former Chelsea striker Chris Sutton told BBC Radio 5 Live’s Monday Night Club.
“He has had a brilliant career but, at 30, he has to prove himself again.
“The Chelsea thing is baffling in some respects, that he seemed to be frozen out and Chelsea have a striker crisis, yet they weren’t bringing him back into the fold which was slightly odd.”
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